In the theoretical case of US actually invading Greenland (whatever that would mean, considering the largest city Nuuk is the size of a middle-sized town), the question isnt about potential casualties on Greenland.

The question is what would happen to the US staff land-locked on NATO bases within the EU. They will automatically become under siege, vastly outnumbered by European counterparts.

Since any attack on Greenland is an attack on the EU country the Kingdom of Denmark, and any attack on any EU countries automatically trigger EU Article 42.7, which mandates the full support from all members, to which all EU countries have committed, it would imply full-scale war.